We attempt to indirectly deduce the form of quantum geometry on the M5-brane in the presence of a constant C-field 3-form potential. We first show how the noncommutative geometry on the D3-brane in a constant 2-form B-field can be deduced by analysing open strings ending on the D3-brane. We show that the string boundary condition is a modified Nahm equation, and that these modifications can be understood in terms of the noncommutative geometry. Similarly, the boundary condition for M2-branes ending on the M5-brane is given by the Basu-Harvey equation, modified by the C-field. By an analogy, we interpret this modification in terms of a proposed quantum geometry on the M5-brane. This geometry is specified by a 3-bracket, unlike the usual 2-bracket for noncommutative geometry.